Ratio and Fractions

In a Nutshell

A ratio can be turned into fractions by dividing each part by the total number of parts.

Ratios and fractions are closely linked. If a ratio is a:ba : b, the total number of parts is a+ba + b, so:

Fraction of first=aa+bFraction of second=ba+b\text{Fraction of first} = \frac{a}{a + b} \qquad \text{Fraction of second} = \frac{b}{a + b}

For example, the ratio 3:53 : 5 means 8 parts in total. The first quantity is 38\tfrac{3}{8} of the whole and the second is 58\tfrac{5}{8}.

The bar model shows the ratio split into parts. Think of each section as a fraction of the whole bar.

Ratio bar model A bar split into 8 equal parts. 3 parts are shaded in the accent colour and 5 parts in a secondary colour, showing the ratio 3:5. 3 5 Ratio 3 : 5

Change the values. The left portion is always leftleft+right\dfrac{\text{left}}{\text{left} + \text{right}} of the bar.

Watch it work

Question: In a bag of 40 counters the ratio of red to blue is 3:53 : 5. What fraction are red? How many red counters are there?

Have a go

Q1. The ratio of boys to girls is 2:32 : 3. What fraction of the group are boys?

Q2. A drink is mixed in the ratio cordial to water 1:41 : 4. What fraction is cordial?

Q3. The ratio of orange to apple juice is 5:35 : 3. There are 200 ml in total. How many ml of apple juice are there?

Q4. Sand and cement are mixed in the ratio 4:14 : 1. What fraction of the mix is cement?

Q5. In a class of 30, the ratio of students who prefer football to netball is 7:37 : 3. How many prefer netball?